# st: Interaction terms in 2SLS

 From Glenn Hoetker <[email protected]> To "Statalist@Hsphsun2. Edu" <[email protected]> Subject st: Interaction terms in 2SLS Date Sun, 13 Mar 2005 11:02:56 -0600

```I am facing the following problem and hope someone can help me with it.
I have the following model, and do not believe Y1 is exogenous in the
second equation.

Y1=X1 + X2
Y2=X3 + Y1 + Y1*X3

This seems like a classic application for 2SLS, but I can't use a
prepackaged 2SLS routine, since estimating the second equation requires
calculating (Y1_hat*X3). One approach would seem to be doing 2SLS
manually by modeling

Y1_hat=X1 + X2 + X3

and use the results to then estimate the second equation as

Y2=X3 + Y1_hat + Y1_hat*X3.

Several questions:

1.  Is this approach valid in general?
2.  If so, how would one calculate the standard errors for the second
equation?
3A.  In terms of identification, do I have to count both Y1 and Y1*X3 as
endogenous variables?
3B.  If the answer to 3A is yes, can I follow the approach I outlined
above, or do I actually need to estimate two first stage equations
(recognizing that my simplified model has identification problems):

Y1_hat=X1 + X2 + X3
(Y1*X3)_hat=X1 + X2 + X3

with a second stage equation of

Y2=X3 +  Y1_hat + (Y1*X3)_hat ?

Any suggestions, references, or ideas for alternative modeling
approaches would be very, very appreciated.  Many thanks in advance.

Glenn

Glenn Hoetker
Assistant Professor of Strategy
University of Illinois at Urbana-Champaign
217-265-4081
[email protected]

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